Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22551533 | C2 | semidirect |
| 2. C2×C16×D257 | C2 | semidirect |
| 3. #30656974 | C2 | semidirect |
| 4. #30656970 | C2 | semidirect |
| 5. #30656562 | C2 | semidirect |
| 6. #30656539 | C2 | semidirect |
| 7. #357×C257 | C2 | semidirect |
| 33. #16861593 | D4 | semidirect |
| 67. C2×D257 | D16 | semidirect |
| 79. C257 | #2215 | semidirect |
| 87. #357 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551533 | 2 |
| C2×C16×D257 | 2 |
| #30656974 | 2 |
| #30656970 | 2 |
| #30656562 | 2 |
| #30656539 | 2 |
| #357×C257 | 2 |
| #2215 | 257 |